Non-vanishing of Class Group L-functions for Number Fields with a Small Regulator

2019/01/20 by Ilya Khayutin, Khayutin, Ilya
Computer Science · Mathematics · #11E45 #11M41 #Advanced Algebra and Geometry #Analytic Number Theory Research #Coding theory and cryptography #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1901.06710

openalex publication_date 2019/01/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E/ℚ be a number field of degree n. We show that if Reg(E)≪_n |Disc(E)|^1/4 then the fraction of class group characters for which the Hecke L-function does not vanish at the central point is ≫_n,ε |Disc|^-1/4-ε. The proof is an interplay between almost equidistribution of Eisenstein periods over the toral packet in PGL_n(ℤ)\backslashPGL_n(ℝ) associated to the maximal order of E, and the escape of mass of the torus orbit associated to the trivial ideal class.

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